$\mathbb{Z}_3$ parafermionic zero modes without Andreev backscattering from the $2/3$ fractional quantum Hall state

TL;DR

This paper proposes a new method to realize $ ext{Z}_3$ parafermionic zero modes using a superconducting quantum dot array on a fractional quantum Hall edge, avoiding the challenging crossed Andreev reflection process.

Contribution

It introduces a novel superconducting quantum dot array structure that enables parafermionic zero modes through coherent forward scattering, bypassing the need for crossed Andreev reflection.

Findings

Coherent forward scattering has been experimentally demonstrated.

Array size of about ten can tune into parafermionic degeneracy.

The proposed setup simplifies realization of parafermionic zero modes.

Abstract

Parafermionic zero modes are a novel set of excitations displaying non-Abelian statistics somewhat richer than that of Majorana modes. These modes are predicted to occur when nearby fractional quantum Hall edge states are gapped by an interposed superconductor. Despite substantial experimental progress, we argue that the necessary crossed Andreev reflection in this arrangement is a challenging milestone to reach. We propose a superconducting quantum dot array structure on a fractional quantum Hall edge that can lead to parafermionic zero modes from coherent superconducting forward scattering on a quantum Hall edge. Such coherent forward scattering has already been demonstrated in recent experiments. We show that for a spin-singlet superconductor interacting with loops of spin unpolarized $2/3$ fractional quantum edge, even an array size of order ten should allow one to systematically tune into a parafermionic degeneracy.